1. Field of the Invention
The invention relates to random number generators.
2. Description of the Background
A Random Number Generator (RNG) is a variable X whose value takes on a sequence of numbers in which the probability of any particular sequence is equally likely. The idea of random number generation refers to the probability of generation of any sequence being equal.
Random numbers mean sets or sequences of numbers generated by a RNG.
Pseudo-random numbers mean any distribution or sequence of numbers produced by a deterministic algorithm. Conventional software-based random number generators (RNGs) produce pseudo-random numbers.
True-random numbers mean any distribution or sequence of numbers relying upon randomness in physical or natural events believed to provide random events. Thermal noise in electronics and radioactive decay are believed to provide truly random events.
Herein, the symbol τd defines the dead time or recovery time of a detector.
A single photon detector means a detector with a substantial probability of detecting the existence of a single photon.
APD herein means an avalanche photodetector. An APD may be a single photon detector.
An APD dead time, τd, is a duration of time after a detection event during which the APD remains inactive or unable to respond fully to light incident on the APD.
APDs can be designed to operate (detect photons) in spectral windows spanning 850 nm, 1310 nm, and 1550 nm. Silicon, Germanium, and InGaAs APD detectors are common. R. G. Brown, K. D. Ridley, and J. G. Rarity, Appl Opt 25, 4122 (1986) and Appl Opt 26, 2383 (1987) describes an APD reverse-biased above breakdown in Geiger mode that has a dead time τd,.
Effective dead times means a duration of time after a detection event during which the detector fails to respond fully to incident light due to “after-pulse” effects.
After pulse effects in APDs occur, particularly InGaAs/InP APDs sensitive at 1550 nm, due to charges trapped after a detection avalanche in an APD. After pulsing effects are described in M. Bourennane et al., Optics Express 4, 383 (1999); A. Karlsson et al., Circuits and Devices 11, 34 (1999).
Rapidly quenching the avalanche in an APD reduces the APDs dead time. Passive avalanche quenching means quenching the avalanche in an APD using passive electronic elements. Dead times for typical passively quenched APDs are 1 μs. Active quenching means quenching the avalanches in an APD using active electronic circuits.
A gated mode reduces dark count rates in a detector, such as an APD. The gate duty cycle in the prior art of APD usage comprises one short time window of the order of the pulse duration for detection followed by a long time window on the order of the dead time τd. See M. Bourennane et al., J Mod Opt 47, 563 (2000). A pulsed light source's repetition rate 1/τs, can be changed relatively easily and can be orders of magnitude larger than the detector recovery rate 1/τd. Light sources that can be used in conjunction with APDs include LEDs, visible and infrared lasers, and vapor lamps. Imperfect detectors (with non-unity detection efficiency) and channel losses can be lumped into an effective transmission coefficientη=ηtransηdetector.  (1)The light transmission channel may be any medium or means, such as free space, optical fiber, or waveguide, to convey electromagnetic signals from a source to a detector. Typical detector efficiencies ηdetector are 50–75% for silicon APDs detecting light at 600–850 nm and 10–15% for InGaAs APDs at 1550 nm.
The publication by A. Stefanov et al., at URL: http://xxx.lanl.gov/abs/quant-ph/9907006, proposes detecting weak optical signals using single photon detectors as a method of generating true random numbers. Stefanov et al. proposes a pulsed light-emitting diode (LED) attenuated to average photon number ñ<<1, two optical paths in fiber, and one passively quenched APD for single photon detection. The apparatus splits the signal pulse between the two optical paths, one short and one long, to the detector. This creates two possible arrival time slots at the detector, one for each path, which are assigned bit values 0 and 1. Only a signal from one path or the other causes a detection event, but exactly which path per pulse triggers this detection is a random process. By using an electronic clock and logic circuit, the apparatus reconciles the successful detection of a signal at one time slot or the other with the transit time from source to detector, producing one bit per detection event. The Stefanov et al. proposed method alternates between an active and inactive period, τtotal=τa+τi, where τa denotes the active period and τi the inactive, for each detection cycle. Their apparatus pulses the source once per cycle so that a photon on the short path arrives at the beginning of the active period. Stefanov and coworkers use an active period of τa≈70 ns with photons on the split paths set to arrive at the detector only during 10 ns time windows at either end. They use a passively quenched detector with τd≈1 μs. Stefanov and coworkers set the inactive period to be equal to the dead time τd. To synchronize the system, the method employs a source period τs that is equal to τtotal: the source and detector run at the same clock speed.
The present inventors calculated the RNG rate of Stefanov's method. Their method determines the random number generation rate. Their Poisson-distributed photon number source with small average photon number ñ gives a rateR=(1−e−ηñ)/τs≈ηñ/τtotal.  (2)Stefanov and coworkers set ηñ to be ˜0.1. The random bit generation rate from (2) is R≈100 kHz.
P. Townsend in patent PCT/GB95/01940 (US005953421) and IEEE Photonics Technology Letters 10, 1048 (1998), demonstrate schemes to distribute quantum signals as a cryptographic key over a kilometer or more of optical fiber. Quantum cryptography requires a quantum channel between source and detector, which means a channel that does not degrade the quantum information (e.g., polarization and/or phase) encoded in the signal pulses. For example, photo detection occurs in an actively quenched APD without gating and with τd≈50 ns. See IEEE Photonics Technology Letters 10, 1048 (1998), which discloses a system wherein a photon can arrive at the detector during two distinct time slots, corresponding to bit values 0 or 1. The pulse period τs is 2.5 ns. The losses and average photon number effectively give ηñ˜0.006, yielding an average count rate of 2.4 MHz and quantum bit rate R≈1.2 MHz.